Average consensus algorithms robust against channel noise

Average consensus algorithms have attracted popularity in the wireless sensor network scenario as a simple way to compute linear combinations of the observations gathered by the sensors, in a totally decentralized fashion, i.e., without a fusion center. However, average consensus techniques involve the iterated exchange of data among sensors. In a practical implementation, this interaction is affected by noise. The goal of this paper is to bring some common adaptive signal processing techniques into the sensor network context in order to robustify the iterative exchange of data against communication noise. In particular, we will compare the performance of two algorithms: (a) a method, reminiscent of stochastic approximation algorithms, using a decreasing step size, with proper decaying law, and (b) a leakage method imposing that the consensus cannot be too distant from the initial measurements. We provide a theoretical analysis, validated by simulation results, of both methods to show how to derive the best tradeoff between the system parameters in order to get the minimum estimation variance, taking into account both observation and interaction noise.